Regularized sparse representation for image deconvolution

Abstract

An image deconvolution approach based on regularized sparse representation is proposed. Given an observed blurred image, traditional deconvolution approach based on sparse representation constructs the 1 -norm regularization directly by using the direct observed model and the sparsity of image decomposed on a redundant dictionary. However, the 1 -norm regularization has large coherence because of the compactness of the blurring operator. Therefore, we multiply the blurred image with a regularizing operator and construct the 1 -norm regularization by using the converted data. The approach, referred as regularized sparse representation, possesses the following merits: (i) it decreases the coherence of the 1 -norm regularization; (ii) algorithm solving the regularization is fast converged due to the preconditioning strategy. Experimental results demonstrate that comparing with existed state-of-the-art approaches, the proposed approach can obtain good results in terms of speed and deconvolution performance.